Damage accumulation in random loads.

Abstract

An equivalent constant amplitude fatigue loading (Miner's stress) is developed for stationary random amplitude loadings. The effects of rainflow cycle counting and fatigue crack closure are included. A method for determining the opening stress in a random loading is also proposed. This research takes a fatigue damage factor approach. The damage factor is defined as the ratio of the wide band rainflow fatigue damage to the equivalent narrow band fatigue damage. The mathematical form of the damage factor equations is derived from theoretical derivations using the analytically tractable local range cycle counting method. Simulations of stationary Gaussian random processes are used to empirically derive the values of certain parameters dependent on the spectral shape for the rainflow cycle counting equations. There are five tasks in this research. (1) A simulation program for generating a Gaussian process has been written and is used to generate random loading histories for this study. (2) A previously proposed rainflow damage factor has been verified and refined with these simulations, without considering crack closure. (3) Using a sinusoidal approximation, the joint probability density functions between peaks, valleys and rises counted by the local range method are derived. (4) The resulting joint probability distributions are used to determine the theoretical damage with crack closure; simulations are again used to calibrate the parameters for rainflow stress cycles. (5) A procedure for finding an equivalent constant fatigue crack opening stress for stationary random loadings is described. An example application of the procedures and equations is given.